Represents a 2-sphere made from two faces glued together along their three edges.
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Public Member Functions |
NPillowTwoSphere * | clone () const |
| Returns a newly created clone of this structure.
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NFace * | getFace (int index) const |
| Returns one of the two faces whose boundaries are joined.
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NPerm4 | getFaceMapping () const |
| Returns a permutation describing how the boundaries of the two faces are joined.
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void | writeTextShort (std::ostream &out) const |
| Writes this object in short text format to the given output stream.
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| ShareableObject () |
| Default constructor that does nothing.
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virtual | ~ShareableObject () |
| Default destructor that does nothing.
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virtual void | writeTextLong (std::ostream &out) const |
| Writes this object in long text format to the given output stream.
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std::string | toString () const |
| Returns the output from writeTextShort() as a string.
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std::string | toStringLong () const |
| Returns the output from writeTextLong() as a string.
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Represents a 2-sphere made from two faces glued together along their three edges.
The two faces must be distinct and the three edges of each face must also be distinct. Neither of the faces may be boundary faces. These two faces together form an embedded 2-sphere in the triangulation (with the exception that two or three points of the sphere corresponding to the face vertices may be identified).
This 2-sphere can be cut along and the two resulting 2-sphere boundaries filled in with 3-balls, and the resulting triangulation has the same number of tetrahedra as the original. If the original 2-sphere was separating, the resulting triangulation will contain the two terms of the corresponding connected sum.
NPerm4 regina::NPillowTwoSphere::getFaceMapping |
( |
| ) |
const |
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inline |
Returns a permutation describing how the boundaries of the two faces are joined.
The permutation will map vertices (0,1,2) of getFace(0)
to vertices (0,1,2) of getFace(1)
. The map will represent how the vertices of the faces are identified by the three edge gluings.
- Returns:
- a permutation describing how the face boundaries are joined.